Blender scripting GPU acceleration
You should be able to using existing python libraries, such as pycuda, which can be installed into blender's built in python (for installing libs you could setup pip or whatever: How to install Pip for Blender&#39;s bundled Python?). You can also link an C/C++ program from your script and do it there. 

You will always, however, be limited by the speed in which you can use python to transfer data too and from blender's internal format, so this may or may not provide much speedup depending on your use case.

Gpus can provide a speedup to some kinds of operations. In general, code for that operation needs to be specifically written for use on a gpu to take advantage of it. If you wanted to accelerate existing blender functionality you would have to rewrite it to run on the gpu, you can't just magically tell cpu code to run on the gpu instead.

In general, only tasks with many repetitive, independent, but similar math operations work well on GPUs. Because of these restrictions, GPU code and algorithms are generally more difficult to create than just for the CPU.